The greatest discoveries in astronomy have come with advancements in ground-based observatories and space telescopes. Latest trends in ground-based observatories have been ever increasing size of the primary mirror, providing much higher apertures for more powerful image captures. The same trend can be envisioned for space telescopes. In fact, concepts for ultra-large space telescopes (ULST) on the order of hundreds of meters in size have been emerging since the late 1990's and early 2000's. Currently, James Webb Space Telescope (JWST) scheduled to be launched in 2014 only has primary mirror diameter of 6.5 m. An important issue in the ULST is correcting for optical errors caused by large thermal deformations expected due to exposure to radiation in orbit. As of now, there are no methods for solving technical complexities involved in correcting for such deformations. Furthermore, the costs associated with weight, deployability, and maintenance hinder advancements in large space telescopes. This thesis explores the idea of using binary actuators coupled with elastic elements to offer solutions to these problems. The feasibility of using binary actuators with elastic elements for correcting the focus of the deformed structure is investigated. The investigation begins with simple representations of the primary mirror structure in one-dimensional study, then in two-dimensional study for planar analysis. The analysis includes exploration of the workspace, demonstration of deterioration of superposition, and performance measured in precision of focus correction. In general, the number of actuators required for an acceptable level of correction is about three times the number of degrees-of-freedom in the system. Ultimately, it is concluded that in the planar domain it is feasible to use binary actuators in the control of primary mirror structure for large space telescopes.
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